Space of modular forms of level 8, weight 11, and Character 8.d

• Label: 8.11.d
• Level: $8$
• Weight: $11$
• Character orbit: 8.d
• Rep. character: $\chi_{8}(3,\cdot)$
• Character field: $\Q$
• Dimension: $9$
• Newform subspaces: $2$
• Sturm bound: $11$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 8 = 2^{3} \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	8.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 8 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(11\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{11}(8, [\chi])\).

	Total	New	Old
Modular forms	11	11	0
Cusp forms	9	9	0
Eisenstein series	2	2	0

Trace form

9 * q + 10 * q^2 - 2 * q^3 + 1236 * q^4 + 10012 * q^6 - 32840 * q^8 + 137779 * q^9 + 9120 * q^10 + 45902 * q^11 - 313448 * q^12 - 400320 * q^14 - 938736 * q^16 + 452882 * q^17 - 2477042 * q^18 + 5107038 * q^19 + 2557440 * q^20 + 4666812 * q^22 - 4000112 * q^24 - 9027135 * q^25 + 1891680 * q^26 - 26107748 * q^27 + 18286080 * q^28 + 67026240 * q^30 - 97571360 * q^32 - 27349372 * q^33 - 142063212 * q^34 + 53736960 * q^35 + 228065116 * q^36 + 267808988 * q^38 - 357584640 * q^40 + 54890402 * q^41 - 576155520 * q^42 + 204294990 * q^43 + 628067288 * q^44 + 851947200 * q^46 - 1648174112 * q^48 + 202043001 * q^49 - 1981861190 * q^50 - 673729540 * q^51 + 2420759040 * q^52 + 3511590520 * q^54 - 2928529920 * q^56 - 215783068 * q^57 - 3245264160 * q^58 - 44598418 * q^59 + 5250055680 * q^60 + 4060980480 * q^62 - 4730963904 * q^64 - 839028480 * q^65 - 7472960920 * q^66 + 588125502 * q^67 + 6101561768 * q^68 + 7723829760 * q^70 - 10021483928 * q^72 + 1194291138 * q^73 - 7669373280 * q^74 - 221476850 * q^75 + 7187666712 * q^76 + 7176312000 * q^78 - 6408629760 * q^80 + 4396660573 * q^81 - 2429852748 * q^82 + 1949474078 * q^83 - 2916218880 * q^84 - 3841359172 * q^86 + 9008033808 * q^88 - 4953423262 * q^89 + 12545940960 * q^90 + 7645985280 * q^91 - 8903892480 * q^92 - 14182177920 * q^94 + 24050761792 * q^96 - 19570841550 * q^97 + 25720660330 * q^98 - 30528237382 * q^99

Decomposition of \(S_{11}^{\mathrm{new}}(8, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
8.11.d.a	$8$	$11$	8.d	8.d	$2$	$1$	$1$	$5.083$	\(\Q\)	\(\Q(\sqrt{-2}) \)	✓	✓			8.11.d.a	$2$	$0$	\(-32\)	\(-482\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q-2^{5}q^{2}-482q^{3}+2^{10}q^{4}+15424q^{6}+\cdots\)
8.11.d.b	$8$	$11$	8.d	8.d	$2$	$8$	$8$	$5.083$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None		✓	✓		8.11.d.b	$2$	$0$	\(42\)	\(480\)	\(0\)	\(0\)	$2^{28}\cdot 3^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(5-\beta _{1})q^{2}+(60+\beta _{1}+\beta _{2})q^{3}+(5^{2}+\cdots)q^{4}+\cdots\)